3.6 Approximation of the Self-Energy

However, using non-interacting GREEN's function in self-energies, which is
referred to as *BORN approximation*, is not fully consistent, since the
background particles contributing to the self-energy are treated as
non-interacting. In reality, of course, these particles also move in an average
potential coming from the presence of all the other particles. Thus instead of
non-interacting GREEN's functions (single lines), one has to use the exact
GREEN's function (double line) in the proper self-energy, as shown
in Fig. 3.9. Since the exact GREEN's function both
determines and is determined by the proper self-energy , this
approximation is known as the *self-consistent BORN approximation*
(see Appendix F.3). The self-consistent approach preserves
conservation laws (Appendix F.3), for example, the
continuity equation holds valid (Section 3.9.4). Throughout this work the
self-consistent BORN approximation is applied.